The singular value decomposition (SVD) of polynomial matrices plays a pivotal role in the analysis and optimisation of broadband multi-input multi-output (MIMO) systems. In this paper, we present novel algorithms for performing the SVD of polynomial matrices that utilise a sequential matrix diagonalisation (SMD) approach. The proposed approach commences with the identification of a column (or row) exhibiting the highest off-diagonal energy through a maximum search procedure. This energy is subsequently transferred, utilizing a delay operation, to the zero-lag coefficient matrix, which is then diagonalized via a standard SVD. This procedure is iterated until the maximum off-diagonal element falls below a predetermined threshold. We introduce multiple algorithmic variants that offer different convergence speeds and demonstrate their superior performance over the prior art. Our contributions include rigorous convergence proofs and a comprehensive comparison of computational efficiency and diagonalisation accuracy. Extensive simulations on randomly generated polynomial matrices with Gaussiandistributed coefficients validate the robustness and efficacy of our GSMD approach, making it highly suitable for real-world broadband MIMO applications.